Answered: Penelope utility function is U (a, b) =…

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics

Section: Chapter Questions

Problem 5WNG

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Question

Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of apples
consumed and b is the amount of bananas consumed. He has $100 income. The
price of apple is $0.5 per lb. Price of banana’s though increases with its purchase.
Specifically, buying, b pounds of bananas will cost Pedro b2.
a. What is Penelopes optimal consumption?
b. Now, he suddenly acquires an extra $100 income. How this will change
his allocation?

Expert Solution

Step 1

Utility function : U (a, b) = a+ 10b−b²

Income = 100

b pounds on banana cost = b²

1 pound of banana would cost = b²/b

=> b

Therefore , Price of banana = b

Budget Constraint : Pa *a + Pb *b = Income

=> 0.5 a + b² = 100

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